In this paper we investigate channel state information (CSI) feedback strategy for a basestation (BS) scheduling multiple users for data transmissions in the downlink. For the purpose of fair provisioning of service among users with possibly heterogeneous channel statistics, we adopt scheduling algorithms based on scores: specifically the maximum quantile (MQ) scheduling is used as one of such schedulers where the score corresponds to the quantile of instantaneous SINR. Our feedback scheme is based on contention where we would like to guarantee a set of arbitrary long-term average scores to users and study feedback methods which enable such assignment. We show how the scores are assigned in a maximal manner leveraging the framework of maximum weight schedulers. The problem turns out to be nonconvex, however for two users case we present an explicit formula of feedback for the optimal score assignment. We derive the expression for the optimal feedback parameters which turn out to be asymmetric among users. We analytically show that, even for contention based feedback, by optimally tuning the feedback parameters one can perform very close to feedback scheme without contention. A numerical result is provided in support of the analysis.